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Maths Interview Questions-HELP!

Right guys, how would you approach and answer these maths/interview questions in an interview ( need to know, p.s model answers very much appreciated if possible, also i have attempted some of the questions but i end up leading to no where, by the way does anyone know how i can improve my lateral thinking?)

1)Is mathematics a language?
2)Describe a complex number to a non-mathematician?
3) How many ways are there of arranging n objects and why?
4)Which is bigger, ' e to the power of pi' or 'pi to the power of e'?
5)How do you predict a Pythagorean triple?
6) Explain the difference between science and technology?
7) Each room in a house has a number of doors leading out of it. Prove that the exterior of the house has an even number of doors.
8)Prove 'e' is irrational
9) Differentiate x to the power of x

Reply 1

j1i9s9s5

Original post by Omar.Q

Number 9

Unparseable latex formula:

let \ $y \ = \ x^{x}=e^{lnx^{x}}=e^{xlnx}$\\[br][br][br]$\frac{d(e^{f(x)})}{dx}=f'(x)e^{f(x)}$\\[br][br]$\frac{dy}{dy}=(lnx+1)e^{xlnx}=(lnx+1)x^{x}$

(edited 10 years ago)

Reply 2

Omar.Q

Original post by j1i9s9s5

Unparseable latex formula:

let $y=x^{x}=e^{lnx^{x}}=e^{xlnx}$

Now we can differentiate this using the rule:

Unparseable latex formula:

$\frac{d(e^{f(x)})}{dx}=f'(x)e^{f(x)}$

Which gives us:

Unparseable latex formula:

$\frac{dy}{dy}=(lnx+1)e^{xlnx}=(lnx+1)x^{x}$

can you tell me which core unit this level of maths is from, and what rule it is, because i'm not familiar with it, as i havent studied all of A2 yet
thanks in advance :smile:

Reply 3

Omar.Q

Moving this post to maths forum, http://www.thestudentroom.co.uk/showthread.php?t=2413750&p=43674573#post43674573

Reply 4

Omar.Q

Original post by j1i9s9s5

I don't know I just made it up now. :smile:

O.o made it up?

Reply 5

Tedward

Original post by Omar.Q

can you tell me which core unit this level of maths is from, and what rule it is, because i'm not familiar with it, as i havent studied all of A2 yet
thanks in advance :smile:

I think its C3, the method for differentiating xlnx is the product rule. Another method would be to ln the equation

y=x^x

giving

ln(y)=xln(x)

and then implicitly differentiating which i think may be C4...

Reply 6

Omar.Q

Original post by Tedward

I think its C3, the method for differentiating xlnx is the product rule. Another method would be to ln the equation

y=x^x

giving

ln(y)=xln(x)

and then implicitly differentiating which i think may be C4...

I have not studied C4 yet, and have briefly done C3, so this may pose a problem lol

Reply 7

Tedward

Original post by Omar.Q

I have not studied C4 yet, and have briefly done C3, so this may pose a problem lol

yeah well the product rule isnt that complicated. it simply says that [latex/]\dfrac{d}{dx}f(x)g(x)=f(x)\dfrac{d}{dx}g(x)+g(x)\dfrac{d}{dx}f(x) so in this case f(x)=x and g(x)=ln(x)

Reply 8

Tedward

Original post by Omar.Q

2)Describe a complex number to a non-mathematician

I'd say this but its by no means the best way to explain..im not great at explaining maths...

A complex number is a number made up of a real number and an imaginary number. it has the form C=a+bi. Real numbers (a,b) are normal numbers that you use everyday. Imaginary numbers (i)are formed by square rooting -1.

Doing this normally isn't allowed because no real number squared will equal a negative.

x^2\geq0

when x is real. That is why the new type of numbers called "imaginaries" are used which do have this property.

This may seem strange and kind of like cheating just to create a number to make something work. however just because it has no physical quantity doesn't mean it shouldn't be used. negative numbers have no physical quantity and there was a time when people thought the idea of them was absurd. we don't hesitate nowadays, in the same way Mathematicians don't hesitate to use imaginary numbers.

hope that helps.

(edited 10 years ago)

Reply 9

davros

Original post by Omar.Q

Questions 1, 2 and 6 are designed to test how YOU think, so there is no "model answer" to them, and no-one can tell you what the right answer (if there is one) should be!

Question 9 is straightfoward once you've covered the relevant methods of differentiation either in C3 or C4.

Q3 is something you should be able to work out for yourself - if not, have a look at Permutations and Combinations (often taught as part of S1) because it's standard bookwork.

Here's a hint for Q4: do you know how to work out the maximum value of (ln x)/x and where it occurs?

Q7 - are you sure you've quoted this correctly? What happens if you have a single-room house with one exterior door? Check the question and then play around with some diagrams!

Q8 is not something you are going to be asked to reproduce in an interview - an interviewer or examiner may try to lead you through the method with guided questions but you wouldn't be expected to come up with the proof by yourself! If you're interested, there are introductory university texts where you can look up the standard proof of the irrationality of e.

Hope this helps!

Reply 10

Omar.Q